Question

Select the correct answer.

Which function is the inverse of f(x) = (x - 3)² + 2?
¹(z)=√x - 2 + 3
f¹()=√x +3 - 2
f¹(z)=√x + 2-3
¹(z)=√x - 3+ 7
OA.
OB.
O c.
O D.

Answer 1

The correct inverse function of f(x) = (x - 3)² + 2 is f⁻¹(z) = √x - 2 + 3, by reversing the operations applied to x and using the principal square root.

Step-by-step explanation:

To find the inverse function of f(x) = (x - 3)² + 2, we need to reverse the operations that have been applied to x. Here is a step-by-step process:

1. Let y = (x - 3)² + 2.
2. To find the inverse, swap x and y to get x = (y - 3)² + 2.
3. Solve for y by first subtracting 2 from both sides: x - 2 = (y - 3)².
4. Take the square root of both sides: √x - 2 = ±(y - 3).
5. We usually consider the principal square root for the function to pass the vertical line test, so we have √x - 2 = y - 3.
6. Finally, solve for y to get y = √x - 2 + 3, which is the inverse function.

Hence, the correct answer is f⁻¹(z) = √x - 2 + 3.